Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

learn more… | top users | synonyms (1)

0
votes
0answers
24 views

Can someone explain the steps to the solution in detail please

I've got this question here. I already have the solution but I have no idea how the solution came up. Can someone share any steps in detail for dummies to understand the logic behind it. Any video any ...
1
vote
1answer
15 views

How to know for sure this is a low-pass filter

Given the transfer function $$H(z) = \frac{1}{4}(1+z^{-1}+z^{-2}+z^{-3})$$ I understand I have to switch $z$ to $e^{j\Omega}$, $0\le\Omega\le\pi$, in order to find out how it interacts with ...
0
votes
1answer
18 views

Constructing a 2 fold oversampled cosine basis in MATLAB

So I'm trying to construct a 2 fold oversampled cosine basis in MATLAB. I know how to construct the basis as a square matrix using the following command: $\mbox{dct(eye($n,n$))}$ where dct is the ...
4
votes
0answers
73 views

Best sources on complete transforms (classic orthonormal transforms) and overcomplete transforms in signal processing

In the introduction section of a thesis I read a little about classic orthonormal transforms such as Fourier, discrete cosine and wavelet transforms and their application in signal processing. Then ...
1
vote
0answers
34 views

Isomorphisms of normed vector spaces

I'm having difficulty with the following question: Show that, for $\mathbb{F} \in \{\mathbb{R}, \mathbb{C}\}$ and for an infinite discrete time-domain $\mathbb{T}$, $\exists$ an isomorphism of normed ...
0
votes
0answers
17 views

Is the sum of all cross-correlation samples representative of target existence likelihood?

Answers to this question take the peak in the cross correlation as the measure to the likelihood of the trigger signal exist in the received signal - this is pretty much text book. My question is ...
0
votes
0answers
16 views

2D convolution with one-dimensional function

I am somewhat stumped on what may be a very basic question. I have a 2D input function $F(x,y)$ and an impulse response $H(x)$ that is independent of $y$. The output function is a convolution ...
1
vote
1answer
71 views

Subderivative of $ ||Au||_{L^{\infty}} $ to compute proximal operator

I am looking for ways to compute the subderivative of $ ||Au||_{L^{\infty}} $, as I want to solve the minimization problem of \begin{equation} \min\limits_u \quad \lambda ||Au||_{L^{\infty}} + ...
0
votes
0answers
17 views

Orthogonalization of two N dimensional signals as a similarity check

I'm trying to find how 'similar' or 'different' two vectors are, in relation to a third vector. Say A and B are features in my data set, with C being the output. I have N data points for each of them ...
0
votes
1answer
32 views

Find Fourier transform of triangular function based on a Fourier results of rectangular

I have a triangular pulse given by $$x\left(\frac{t}T\right) = \begin{cases} 1-\frac {|t|}T, & \text{if $T\ge t$} \\ 0, & \text{otherwise} \end{cases}$$ Given that ...
0
votes
1answer
27 views

Effect of sampling frequency on Discrete Fourier Transform?

I don't get it. I have the following form of the DFT: $$ Y_N(e^{j\omega_n})=\sum_{k=1}^{N-1}y(k)e^{j\omega_n k}\quad\omega_n=\frac{2\pi n}{N}\quad n=0,1,...,N-1 $$ But this assumes that the sampling ...
1
vote
1answer
53 views

Minimum number of zeros of this Laplace transform

I've come across this question in my Signals and Systems class but I can't seem to understand what the answer might be. Here is the entire question: Consider a signal x(t) which has its Laplace ...
0
votes
0answers
11 views

Result of sampling of function with too small fs and reconstruction with square function

everybody I have an exam in signal processing tomorrow and doing past exams to prepare myself however I'm on stuck on a particular problem. It is stated as: Considering an ideal sampling with f_s = ...
3
votes
2answers
98 views

secret formula for the “sin” wave with variable rising/falling edge

My math is pretty much forgotten. I was wondering if someone can take a look at this and share what's the formula for creating something like this. ...
1
vote
1answer
35 views

Find Discrete Time Fourier coefficients of $(-1)^n x[n]$

Given that $x[n]$ is an N-periodic sequence with Fourier coefficients $a_k$, I want to find the Fourier coefficients of $$(-1)^n x[n]$$ for the situation in which $N$ is odd. I'm also interested in ...
0
votes
0answers
23 views

Lost power with apodizing mask

I previously asked a similar question on the signal processing community, but I think may be more easily solved from a mathematical perspective. I start out with an image, $I$. To be able to process ...
0
votes
0answers
35 views

Fourier transforms of random processes

In the Wikipedia article on Brownian noise, the Fourier transform of Brownian noise is determined. How is that Fourier transform defined? It seems it is a non-random quantity there, so it is not ...
0
votes
1answer
62 views

Derivative of unit step function

The ramp function is given by r(t)=tu(t) If we differentiate ramp ,we get unit step function. That is, u(t)=1 So the derivative of unit step function is definitely 0 since u(t) is constant over the ...
0
votes
0answers
20 views

Amplitude vs. Amplitude Spectrum?

I feel like I keep getting confused about amplitudes when talking about signal processing. Maybe someone can help clear my confusion. Lets say I have a simple sinusoid $f(t)=Asin(\omega_0 t)$ The ...
1
vote
2answers
35 views

Confusion with a function transformation

I got a HW problem wrong in my Signals and Systems class and am hoping someone can help me understand why. There's a discrete-time signal ...
0
votes
0answers
12 views

Limits to Discrete Fourier Transforms for Spectral Analysis

I am trying to leverage DFT and IDFT for some noise filtering on some data I am collecting. I am trying to do this in a user friendly/cheap manner by coding this in excel (I know this is not the best ...
1
vote
0answers
33 views

ICA obsession with gaussianity

There are two reasons to focus on "gaussianity". (1) Orthogonal transformations of gaussian distributions are again gaussian. (2) Mixing of signals tends to a gaussian distribution via Central Limit ...
0
votes
0answers
15 views

Error analysis for a non-optimal nonuniform quantizer

I'm new to the theory on the subject of quantization. I'm wondering if there are any references that I can look at on error analysis for a non-optimal nonuniform quantizer. More specifically, I ...
0
votes
1answer
46 views

Is $y[n]=x[n]-x[n-1]$ invertible system?

Well, the title says everything. I know I can find a z-transform, find $H(z)$ and then find a appropriate invert system and comment on that. How do I explain it to a person who does not know ...
1
vote
0answers
12 views

Sampling Theorem for Lattices

I am looking for a reference for an analogue of the Shannon sampling Theorem for more general lattices (in any dimension). Something along the lines of the theorem in this wikipedia article: ...
0
votes
0answers
17 views

Inverse z-transform of $z^4+1.827z^3+2.338z^2+1.827z+1$

I need to transform the following $H(z)$ back to time domain: $$ H(z)=(z-e^{j\frac{8}{15}\pi})(z-e^{-j\frac{8}{15}\pi})(z-e^{j\frac{12}{15}\pi})(z-e^{-j\frac{12}{15}\pi}) $$ I did the following steps ...
1
vote
1answer
126 views

How to determine the states of ideal diodes in simple circuits with only DC sources and resistors [closed]

How can the states of ideal diodes be determined in simple circuits with only DC sources and resistors without a trial and error approach? I posted this question on Electronics SE and found out ...
0
votes
0answers
19 views

Is a signal summable when given a z-transform?

The output of a system is given as z-transform: $$ Y(z)=\frac{1+z^{-2}}{(1+\frac{1}{4}z^{-1})(1-\frac{1}{2}z^{-1})} $$ I want to know if the signal in the time domain is summable, meaning that the ...
0
votes
0answers
43 views

fourier series of unknown functions

I am confused in understanding use of fourier expansions of functions. This answer, for example says that we can write voice as a sum of sines and cosines of different frequencies and amplitudes, but ...
0
votes
1answer
67 views

Is the power of a complex exponential signal always zero?

Is the power of a complex exponential signal always zero? For example say I have the function $ f(t) = Ae^{i\omega t}$ Then, I think power is defined as: $P=\int_{-T/2}^{T/2} f^2(t) dt$ So is it ...
1
vote
0answers
22 views

Do combined waves with non-rational frequencies have a common period?

I am facing a problem where I have two waves combined: \begin{equation} y = A\sin(b_1x)+B\cos(b_2x) \end{equation} Where $ b_1 $ and $ b_2 $ are non-rationals. i.e. \begin{align} & b_1 = ...
0
votes
0answers
12 views

How do I compute the output of this LTI system?

2.11. Consider an LTI system with frequency response $$H(e^{j\omega})=\frac{1-e^{-j2\omega}}{1+\frac12e^{-j4\omega}},\quad-\pi<\omega\le\pi.$$ Determine the output $y[n]$ for all $n$ if the ...
0
votes
0answers
49 views

Convolution between a discrete stochastic signal and a continuous function

I'm trying to find the convolution between a discrete, stochastic signal (for which I have data at each t) and an exponential decay function (which is continuous in t). Now I know that one can ...
0
votes
1answer
45 views

Expressing a function in terms of sinc(t)

Given the function: $S(t) = sin(t/\Delta)/t$ How can one express this function in terms of: $S(t) = sin(t)/t$ Thanks!
0
votes
1answer
45 views

Why do high-frequency dynamics quickly go away in a step response?

As we know, a step input hits all the frequencies of a dynamical system. However, my professor told me today that the high-frequency response is only present for a short time at the very start, and ...
1
vote
1answer
23 views

How does hard clipping change the frequency of a pure sinusoidal signal?

Suppose that we decide to limit the magnitude of a real-valued signal $f(t)$ by maximum cutoff $V_s$. Thus, if $|f(t)| > V_s$, a transformed signal $g(t) = V_s$ or $g(t) = -V_s$ depending on the ...
0
votes
0answers
8 views

Help with solving for difference equation coefficient terms

I am having trouble remembering how to solve for the $a_k$ and $b_k$ terms for a difference equation. (it has been some time since taking a signal processing course, where I first learned) I am trying ...
2
votes
2answers
59 views

Using DTFT to find the sum of $\sum_{n=-\infty }^{\infty }\text{sinc}(n\alpha_1)\text{sinc}(n\alpha_2)$

I am trying to use DTFT (as asked in a problem) to find the following sum $$\sum_{n=-\infty }^{\infty }\text{sinc}(n\alpha_1)\text{sinc}(n\alpha_2)$$ for real $\alpha_1>0$ and $\alpha_2<1$. I ...
0
votes
0answers
20 views

Express covariance function of a sampled process as a fourier transform (help with proof)

I'm wrestling with this theorem in my 'stationary stochastic processes' course.It's about sampling of a continous process and a way of rewriting the covariance function of the sample(I'm not entirely ...
1
vote
1answer
41 views

Calculate Inverse Discrete Time Fourier Transform

Calculate Inverse Discrete Time Fourier Transform of the following where $|a| < 1$: $$ X(e^{j\omega}) = \frac{1-a^2}{(1-ae^{-j\omega})(1-ae^{j\omega})} $$ Plugging this directly into the IDTFT ...
0
votes
0answers
20 views

Derive Symmetry Properties of Discrete Fourier Transform

Using the standard definitions of IDFT and DFT: \begin{align*} x[n] &= \frac{1}{2\pi} \int_\pi^\pi X(e^{j\omega}) e^{j \omega n} d\omega \\ X(e^{j\omega}) &= ...
0
votes
1answer
56 views

Simple Discrete Convolution Question

With the discrete step function $$ u[n] = \begin{cases} 1, & n \ge 0 \\ 0, & n < 0 \\ \end{cases} $$ And the output $y[n]$ defined as a discrete convolution of the input $x[n]$ ...
-1
votes
0answers
17 views

Frequency response of causal linear invariant systems.

So for linear causal invariant systems the $g(k)$ response is $g(k)=0$ for $k<0$ How about the frequency response? Since $G(f)=g(k)e^{-2j\pi f}$ then $G(f)=0$ for $f<0$?
1
vote
1answer
73 views

Series of $\csc(x)$ or $(\sin(x))^{-1}$

In some cases I found that $$\csc(x)= \lim\limits_{k\rightarrow \infty}\sum_{n=-k}^{k}(-1)^{n}\frac{1}{x-n\pi}$$ Is anything to prove or disprove that?
0
votes
0answers
21 views

Variance of estimating coefficients by correlating a sequence

I have a sequence $$ r[n] = a_1.t_1[n] + a_2.t_2[n] + a_3.t_3[n] + ... $$ where $t_1, t_2, t_3,...$ are uncorrelated, two-level (+A/-A), zero mean, pseudo-random sequences. To estimate $a_1$, ...
0
votes
1answer
30 views

Signal processing very short question?

We have $Y(k)=x(k-1)+ kx(k-5)+x(k)^4$ .I have to find the impulse response for the function So I know that $G(z) = \frac{Y(z)}{X(z)}$ but how do I relate that to this? $Y(z)=(z^{-1}) + k(z^{-5})+ ...
0
votes
1answer
47 views

Expected value of product of sinusoids

In the book Adaptive Signal Processing by Widrow, an equation (2.20) on page 23 is presented without proof as: $$E \left[ x_k x_{k-n} \right] = \frac{1}{N} \sum_{k=1} ^{N} \sin\left(\frac{2 ...
0
votes
0answers
41 views

Fourier kernels relations to windowing in signal processing.

In engineering a common practice is to "window" a signal (by multiplying a function which decays smoothly at each end) before applying a Fourier transform. Windowing is done to avoid false frequency ...
0
votes
0answers
35 views

What are the name of these signals

It might be funny but there are two signals which confuse me about how to call them. Signal1: http://s3.postimg.org/ffefhwqyr/Capture1.png Signal2: http://s3.postimg.org/samf4o683/Capture2.png I am ...
0
votes
0answers
28 views

Decompose summation of signals

Imagine a summation of three distinct signals such as in the following graphic. Is it possible to estimate the original signals? Below is a matlab-code to generate the image: I have found similar ...